This talk is a preparation of the necessary tools for proving the non-collapsing
results. The L-length defined by Perelman is the analog of an energy path, but
defined in a Riemannian manifold context. The length is used to define the l
reduced distance and later on, the reduced volume. So far the properties of the
l-length have two applications in the proof of the Poincar´e conjecture. Associated
with the notion of reduced volume, they are used to prove non-collapsing results
and also to study the κ- solutions.